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1. a^2-b^2 = (a+b) (a-b)

2. (a+b) ^2 = a^2 + 2ab + b^2

3. (a-b) ^2 = a^2 -2ab + b^2

4. a+b = b+a [ Commutative property]

5. a + (b+c) = (a+b) +c [Associative Property]

6. a(b+c) = ab + ac [Distributive Property]

7. A + 0 = a [ Identity Property]

8. a * 0 = 0 [Zero Property]

9. FOIL method – (m + n) (x + y) = mn + my + nx + ny

10. Equation of any line with slope m and the y intercept b is given as y = mx + b

11. Equation of line with slope m and one of the co-ordinates lying on the line as (x1, y1) is (y-y1) = m (x-x1)

Let us take some examples where we can apply the Algebra formulas from the sheet.

(3x+4y) ^2

We know that (a+b) ^2 = a^2 + 2ab + b^2

We get 9x^2 + 24xy + 16y^2

Given equation is:-

4y^2 – 36z^2

= (2y) ^2 – (6z) ^2

= (2y + 6z) (2y – 6z) [ a^2 – b^2 = (a + b) (a – b)]

Hence the solution is (2y + 6z) (2y – 6z).